At airports, US Airways, American Airlines and Delta all reported cancellations and the airlines waived fees for Mexico travel.
A quarter of the 50 million doses of Tamiflu stockpiled by the U.S. government has been released and the Obama administration has declared a public health emergency to free up the medicine and federal help to the states who need it.
But pharmacies in several states have been flooded with phone calls from concerned customers.
"Our first phone calls were doctors asking if we had Tamiflu," pharmacist Yvonne Zanpaitella said. "They were prescribing it for their patients and family members."
Symptoms of the swine flu are similar to the regular flu, health officials say, including aching muscles, fever and fatigue. The virus appears to be responsive to medication.
"These drugs do not kill virus, they help prevent its replication and therefore help reduce the symptoms, but they have to be taken within 48 hours so people have to recognize they have a serious illness, get to a doctor and start treatment," said ABC News' Dr. Tim Johnson on "World News." "But we should not be telling people to go out and buy these drugs for use as preventive measure…. We need to reserve drug for actual cases and outbreak."
Overseas, authorities are taking extreme measures to prevent a pandemic. Still scarred by memories of SARS and bird flu, in Japan and China, they're using technology to measures a passengers' body heat, quarantining those arriving from the United States and Mexico with fevers.
In Beijing, thermo graphic cameras and infrared scanners are being used to monitor passengers for a high temperature. Anyone displaying signs of a fever will then be checked by officers and could be quarantined.
In Mexico City, this normally bustling city of 20 million people has been reduced to a virtual ghost town. Schools, museums, parks, even churches have been shut down by the government.
"I haven't been out for days," said one woman, who only left to bring her baby to the doctor for a routine vaccination.
But at least the airport is still open.
"I'm just crossing my fingers that nothing happens in the next four hours and I can get back to the states," said Drew Carlisle, a U.S. tourist from Birmingham, Ala., as he waited for a flight home.
Mexican officials are hoping the 10-day shut-down will be enough to cover the two-day incubation period and the seven-day recovery of anyone who has the virus.
Mark Powell, a photographer from Detroit, lives here with his wife and two children. They can't go out, but are going stir-crazy inside.
"Their schools are canceled so we have to plan some indoor activities, but also you can't invite other kids over," he said. "Shaking peoples' hands, you feel a little self-conscious -- or the traditional kiss in Mexico, a little peck on the cheek."
U.S. Department of Homeland Security Secretary Janet Napolitano said Sunday the government declared a public health emergency, which will allow it to free up resources to tackle the issue.
There is no vaccination for the swine flu strain, which has elements of pig, bird and human strains. But officials said they have ramped up medical surveillance around the country and, as part of the emergency declaration, freed up state and federal resources for prevention. Officials also emphasized the importance of individual care and good hygienic practices.